Performance Evaluation of Two-stage Buffered Production Systems with Discrete General Markovian Machines

Abstract

This paper presents an exact analytical method for the performance evaluation of buffered two-stage production systems where machines are modeled as generally complex discrete time Markov reward models. The method is based on the exact solution of the difference equation describing the dynamics of the system in the internal states. Then, a unique solution is obtained by imposing boundary conditions at the limiting buffer levels. The method results to be computationally stable and efficient even for large number of machine states. The generality of the model allows evaluating a wide set of previously uninvestigated systems. For example, systems with machines having generally distributed failure and repair times, systems with quality deteriorating machines or with flexible machines processing multiple part-types can be modeled. Furthermore, the developed model can be used as a building block to extend the analysis to generally long production lines via system decomposition.